Science & Math Colloquium

Location:

South End Dining Hall

Date:

March 20, 2018

Time:

11:30 AM to 12:20 PM

Description:

Kristin Camenga, Juniata College (and former Houghton professor)

Making the Most of Euler's Formula

Most people remember working with polyhedra in elementary and high school: cubes, prisms, tetrahedra, pyramids, etc. Euler's formula states that if V is the number of vertices, E the number of edges and F the number of faces of a polyhedron, V + F = E + 2.

This is a beautiful and useful formula - but can't we do more? Can we get a similar theorem if we change some of our hypotheses? How does Euler's formula change if we allow polyhedra to be in dimension 4 or 5? or n dimensions? What if we look at angles of polyhedra instead of the number of faces? We will look at several examples as we generalize Euler's formula in these directions and others. We will end with a glimpse of open questions. No specific math background will be assumed, but curiosity is expected!

Houghton College provides an academically challenging, Christ-centered education in the liberal arts and sciences to students
from diverse traditions and economic backgrounds and equips them to lead and labor as scholar-servants in a changing world.